Combinatorial patchworking: back from tropical geometry
We show that, once translated to the dual setting of convex triangulations of lattice polytopes, results and methods from previous tropical works by Arnal-Renaudineau-Shaw, Renaudineau-Shaw, Renaudineau-Rau-Shaw, and Jell-Rau-Shaw extend to non-convex triangulations. So, while the translation of Vir...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
28.09.2022
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Subjects | |
Online Access | Get full text |
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Summary: | We show that, once translated to the dual setting of convex triangulations of
lattice polytopes, results and methods from previous tropical works by
Arnal-Renaudineau-Shaw, Renaudineau-Shaw, Renaudineau-Rau-Shaw, and
Jell-Rau-Shaw extend to non-convex triangulations. So, while the translation of
Viro's patchworking method to the setting of tropical hypersurfaces has
inspired several tremendous developments over the last two decades, we return
to the the original polytope setting in order to generalize and simplify some
results regarding the topology of $T$-submanifolds of real toric varieties. |
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DOI: | 10.48550/arxiv.2209.14043 |